Residue[ArcCoth[z], {z, ComplexInfinity}] == -1

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> res </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> z </ci> </apply> <apply> <arccoth /> <ci> z </ci> </apply> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Residue", "[", RowBox[List[RowBox[List["ArcCoth", "[", "z_", "]"]], ",", RowBox[List["{", RowBox[List["z_", ",", "ComplexInfinity"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", "1"]]]]]]

2001-10-29